Friday, February 12, 2010
Proof vs. Essay: Impossible Convergence?
John Arley Writes in Facebook:
We learned how to do proofs in geometry class, then pretty much that all got ignored for ten years and we focused only on calculations. Why?
My Response (too long to fit in Facebook):
Well, actually, this kind of step-by-step rigor is also supposed to be taught in your English, History, and Economics classes in the form of argumentative essay-writing (ie -- argue a thesis based on a magical synthesis of facts that leads to a larger epiphany not contained within the set of individual facts; which is arguably the concept of a mathematical proof as well). However, the English language, while being a vastly richer and more subtle language than symbolic arithmetic (and thereby capable of communicating an equivalent, if not superior, amount of rigor and complexity) often gets abused by lazy students and teachers who Just Don't Care™ and who instead turn that expressive richness upon itself to create a fertile loam of BS.
There are places where the rigorous essay survives, but very few. It's particularly telling that most complex theoretical mathematics proofs are actually written out longhand, essay-style, and not in the two-column approach taught in Baby Geometry. And in Economics right now, we're having to write essays stepping logically through a sequence of graphical descriptions (basically supply & demand curves) of the interactions of macroeconomic forces to arrive at broader truths about how a stimulus package or spending reduction affects unemployment rates, GDP, price levels, wages, etc. But our professor is pissing everyone off by giving out B-‘s to sloppily argued analyses. “It’s just opinion and BS!,” cries the indignant thought slacker. I wonder how much longer before our professor just switches over to multiple choice questions and gives up on essays altogether.
The real problem is that most everyone seems to have given up on the potential of longhand, non-symbolic language (well, I guess all languages are technically symbolic, but you know what I mean) to construct rigorous arguments and discover higher truths, which is arguably the root cause of the demise of the liberal arts education. These days, a well-written essay is almost universally seen as "opinion" and not "fact," even if it begins with rock-solid assumptions and contains an airtight chain of logical arguments leading to a singular conclusion (or a constrained distribution of possible outcomes). Whereas, an inferior argument, coded in a bare-bones symbolic language, underlain by a basic vagueness of assumptions and bogus constraints, can, as long as it is free of obvious symbolic manipulation errors, oftentimes pass as truth for decades before the underpinning flaws are revealed. And even then, an overturned equation is usually seen as an honest mistake rather than a “gotcha” detection of BS.
So proofs are potentially all around us in high school and as undergraduates (even in -- gasp -- MBA School!), just not necessarily in the same form that we're taught to associate with "proofs." But as our usage of spoken and written language continues to deteriorate, and our confidence in it as a medium of argument declines, we find ourselves only trusting the most barren and simple symbolic languages to derive greater truths, identifying equation derivations as “proofs” in stark relief against the BS of the Essay. The two approaches should be convergent methods of truth discovery but aren’t treated as such and therefore don’t function as such in real-world practice. I’m not surprised, then, that you don’t see proofs everywhere in school. It’s not just for lack of looking, or looking in the wrong places; but that the English-language version of your prey has given up and taken up a postmodern camouflage of vagueness, masquerading as opinion instead of fact, BS instead of logical proof.
The real question is: how did education become all about getting assignments in on time and checking off task boxes instead of critically arguing towards greater understanding? If we could understand that, we might be able to understand how it was that students and teachers stopped taking essay-format proofs seriously. As it is, we only seem to have faith in arguments expressed in the absurdly simplistic language of symbolic logic. Which means that we really only have faith in that which is computationally calculable. A depressing thought indeed for the human species: that our own thought is constrained by the discrete workings of machines. That our larger-than-life thoughts are made in the image and likeness of neural firings collected within synaptic groups instead of being weak representations of infinite truths.
Or is this all just more BS, conjured up within the vagaries of the English language, cheap rhetoric, and sneaky sophisms? If only I could make my argument using a two-column proof, you just might buy into it.
Maybe next time.
posted 9:20 AM | 1 comments
Monday, May 29, 2006
Of Parties and Phone Booths
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Carl Goes Digital, Part III
Plus, outtakes from my exciting Laundromat adventure!
posted 5:48 PM | 2 comments
Friday, May 12, 2006
All bow to the Blue Glow
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Carl goes Digital, Part II
More shots from in and around the 'hood, all taken on my new Nikon D50 with trusty 24mm/2.8 and 50mm/1.8 Nikkor prime lenses.
Due to popular request, this time I've set up the gallery so that the "larger image" is a full-sized 6-megapixel JPG suitable for close-up viewing.
Enjoy!
posted 1:39 AM | 1 comments
Sunday, April 30, 2006
Sit Down, Have Some Coffee, Enjoy
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Carl goes Digital
No, don't settle up on those bets just yet: I haven't converted. I've just added a digital SLR to my ever-growing collection of camera gear: the delightful Nikon D50. My goal in acquiring this camera was to integrate a time-efficient color capture and post-processing workflow into my current, mostly B&W film-and-darkroom process. Some things just look better in color; others demand black-and-white. Why limit myself to the latter fraction of subjects?
Film afficianados, don't fret: for really serious subjects, the D50 will likely be no more than a "rehearsal" or discovery device; when ultimate quality is required, I will still reach for the Hasselblad/Zeiss/Ektrachrome combination to produce the final source negative or positive from which to strike release prints for viewing. Just because digital capture is easy and fun doesn't make it right.
Anyway. Enough blabber. Here are the results of my first weekend out with my new baby. My object in creating these images was to see how close I could come to the look of ultra-saturated reversal film through the judicious use of post-processing techniques; I'm trying to avoid the flat, formica, pasty, purple-fringy look that we all tend to associate with 'digital.' Let me know how well I succeeded in your view!
posted 11:57 PM | 1 comments
Thursday, April 20, 2006
Bill Swanson of Raytheon is a Plagiarist, Part II
Whoops! Looks like the problem runs deeper than I thought.
This incident is not a one-time slip-up on the part of USA Today's fact-checking department -- it's part of a larger effort to publicize the book that Bill Swanson just published: "Swanson's Unwritten Rules of Management." Raytheon's link to order this book is located HERE.
In an earlier promotional interview with Swanson (also published by USA Today), Swanson claims to have created the list of 33 rules himself after working at Raytheon for 33 years.
But perhaps Swanson knows that he shouldn't take the next step and try to SELL his pamphlet to a publisher. Listen in on this interchange:
Q: Publishers have called. Why don't you sell it?
A: We're evalulating that. I've got a full-time job, but my passion is education, so we would have to figure a way to get the proceeds to education, math, and science.
-----
Still, chartible fund-raising intents aside, a man -- particularly the leader of a major US defense contractor -- should not be passing off others' ideas as his own in order to catapult his career to stardom.
Swanson needs to add a 34th rule to his list: Give credit where credit is due.
posted 4:10 PM | 20 comments
Bill Swanson of Raytheon is a Plagiarist!
The following is a letter I submitted this morning to USA Today in response to THIS ARTICLE they ran a few days ago.
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In your article entitled "CEOs say how you treat a waiter can predict a lot about character" by Del Jones, you list 33 "Unwritten Rules" of Raytheon CEO Bill Swanson.
However, it should be mentioned to your readers that nearly all of these "unwritten rules" have indeed been written -- by another author in fact, sixty years ago. Mr. Swanson has plagiarized from the little-known book "The Unwritten Laws of Engineering" by W.J. King (1944, American Society of Mechanical Engineers), trying to pass off others’ work as his own. Perhaps there is a new rule he needs to swallow about taking credit for other people's work. Or perhaps this sort of thing has been his recipe for success in corporate America and, for him, stepping on the genius of others is business as usual.
Here’s just a partial list of the rules that were lifted verbatim from the text of “The Unwritten Laws of Engineering”:
- "Cultivate the habit of 'boiling matters down' to their simplest terms."
- "Do not get excited in engineering emergencies -- keep your feet on the ground."
- "Cultivate the habit of making brisk, clean-cut decisions."
- "Promises, schedules, and estimates are necessary and important instruments in a well-ordered business"
- "Be careful about whom you mark for copies of letters, memos, etc. when the interests of other departments are involved."
- "In dealing with customers and outsiders remember that you represent the company ... be careful of you commitments."
- "Be extremely careful of the accuracy of your statements."
- "Don't overlook the fact that you're working for your boss."
- "Be as particular as you can in the selection of your boss."
- "Strive for conciseness and clarity in oral and written reports."
- "Don't be timid -- speak up -- express yourself and promote your ideas."
- "Confirm your instructions and the other fellow's commitments in writing. Do not assume that the job will be done..."
- "However menial and trivial your early assignments may appear give them your best efforts."
- "In carrying out a project do not wait for foremen, vendors, and others to deliver the goods; go after them and keep everlastingly after them."
The list of similarities and exact quotations goes on and on. This is a particularly serious infraction that deserves the attention and correction of your editorial department.
Sincerely,
Carl Durrenberger, San Diego
Chemical Engineer
posted 3:48 PM | 28 comments
Wednesday, February 22, 2006
A Perfect Dozen
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Golden Hill Walking Tour
Amy and I carouse the streets of Golden Hill while Phil and Janice sketch the home of Amy's old psychiatrist a few blocks away...
This is my first time in about two years trying to shoot Ilford Pan-F 50 Plus. It is a notoriously difficult film to work with, as it exhibits a veritable combination platter of slow speed (nominally 50 ASA, but really closer to 25 or 32), ridiculously high contrast, and incredible developer sensitivity. But, when you master this emulsion, supposedly it sings with rich, buttery, silvery images that withstand mural-size enlargement. I need to tame this wild beast in order to call myself a self-respecting photog.
So anyway, I shot two rolls of the stuff and still don't know what the hell I'm doing.
Be forewarned: the following images are very contrasty. Painfully so. I mean, just LOOK at them: ouch!
posted 12:10 AM | 0 comments
Saturday, February 18, 2006
The Reason for the Neutron Bomb
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University Heights and MOCA-LaJolla
Yet more Olympus Stylus Epic snappies from in and around Twigg's in University Heights as well as last Saturday's quick jaunt with Phil to the Museum of Contemporary Art in LaJolla.
posted 5:26 PM | 0 comments
Irvine vs. Normal Heights
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Irvine Trip & Ray at Night Gallery
Shots from last weekend's sojourn up to Irvine to visit my friend Brian. Note that all these document my Amtrak ride up there, which was great fun and much more photogenic than the final destination. Also, some material from that Saturday's Ray at Night back here in the Normal Heights neighborhood of San Diego. All shot on the classic Nikon FM with 50mm/f2 AI lens on good 'ol Ilford HP5+, rated normally.
posted 5:16 PM | 0 comments
Monday, February 06, 2006
Introducing the Holga
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Twiggs & San Diego Gallery, Door B
Okay, there's only one image from my newly-acquired Holga, but still, it's a new look worth highlighting, isn't it?
Some of these photos were taken by Amy Haven. I've indicated these with an appropriate byline. Except for the Holga image showcased above, all were taken with the Olympus Stylus Epic, with whom I've decided to have many, many babies. Just let me shove it back into my right front pocket.
posted 9:17 PM | 0 comments
